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Proofgold Proof

pf
Apply and3I with 2 ∈ omega, 1 ∈ 2, ∀ x0 . x0 ∈ omega ⟶ divides_nat x0 2 ⟶ or (x0 = 1) (x0 = 2) leaving 3 subgoals.
Apply nat_p_omega with 2.
The subproof is completed by applying nat_2.
The subproof is completed by applying In_1_2.
Let x0 of type ι be given.
Assume H0: x0 ∈ omega.
Assume H1: divides_nat x0 2.
Apply H1 with or (x0 = 1) (x0 = 2).
Assume H2: and (x0 ∈ omega) (2 ∈ omega).
Assume H3: ∃ x1 . and (x1 ∈ omega) (mul_nat x0 x1 = 2).
Apply H3 with or (x0 = 1) (x0 = 2).
Let x1 of type ι be given.
Assume H4: (λ x2 . and (x2 ∈ omega) (mul_nat x0 x2 = 2)) x1.
Apply H4 with or (x0 = 1) (x0 = 2).
Assume H5: x1 ∈ omega.
Apply unknownprop_acdedc0de41048b34117a0d444ff22229a52069432ffb641f4fd684bd4473b0a with x0, x1 leaving 2 subgoals.
Apply omega_nat_p with x0.
The subproof is completed by applying H0.
Apply omega_nat_p with x1.
The subproof is completed by applying H5.
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